Finite Group Databasebeta

← Group #11772296

Character table — Group #11772296

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size1111111122222222222244444444444444444444444444444444444444444444444444444444444444449999999918181818181818181818181836363636363636363636363636363636
order1222444422444444444433666666666666661212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212128888888888888888888816161616161616161616161616161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii
χ511111111111-1-1-1-1-1-1-1-1111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111-1-1-1-1-1-1-1-1111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111-1-1-1-1-1-1-1-1111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii
χ811111111111-1-1-1-1-1-1-1-1111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i
χ91111-1-1-1-1-1-11iiii−i−i−i−i1111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiii−i−i−i−iii−i−i1111-1-1-1-1ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ
χ101111-1-1-1-1-1-11iiii−i−i−i−i1111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiii−i−i−i−iii−i−i1111-1-1-1-1−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζ
χ111111-1-1-1-1-1-11iiii−i−i−i−i1111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiii−i−iii-1-1-1-11111ζ3ζ3−ζ3−ζ3−ζ−ζζζζζ−ζ−ζ−ζ3−ζ3ζ3ζ3
χ121111-1-1-1-1-1-11iiii−i−i−i−i1111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiii−i−iii-1-1-1-11111−ζ3−ζ3ζ3ζ3ζζ−ζ−ζ−ζ−ζζζζ3ζ3−ζ3−ζ3
χ131111-1-1-1-1-1-11−i−i−i−iiiii1111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiiiiiii−i−i−i−iii−i−i-1-1-1-11111ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ−ζζζ
χ141111-1-1-1-1-1-11−i−i−i−iiiii1111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiiiiiii−i−i−i−iii−i−i-1-1-1-11111−ζ−ζζζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζζ−ζ−ζ
χ151111-1-1-1-1-1-11−i−i−i−iiiii1111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−iiiii−i−iii1111-1-1-1-1ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζζ−ζ−ζζ3ζ3−ζ3−ζ3
χ161111-1-1-1-1-1-11−i−i−i−iiiii1111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−iiiii−i−iii1111-1-1-1-1−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3
χ171-1-1111-1-1-11111-1-111-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−ii−ii−iii−i−iii−i−iζ−ζζ−ζζ−ζζ−ζζ3−ζ3ζ3−ζ3ζ3−ζ3ζ3−ζ3
χ181-1-1111-1-1-11111-1-111-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−ii−ii−iii−i−iii−i−i−ζζ−ζζ−ζζ−ζζ−ζ3ζ3−ζ3ζ3−ζ3ζ3−ζ3ζ3
χ191-1-1111-1-1-11111-1-111-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−ii−ii−i−iii−i−iiiζ3−ζ3ζ3−ζ3ζ3−ζ3ζ3−ζ3ζ−ζζ−ζζ−ζζ−ζ
χ201-1-1111-1-1-11111-1-111-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−ii−ii−i−iii−i−iii−ζ3ζ3−ζ3ζ3−ζ3ζ3−ζ3ζ3−ζζ−ζζ−ζζ−ζζ
χ211-1-1111-1-1-111-1-111-1-111-111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111ii−i−iii−i−ii−ii−i−i−iii−i−iiiζ−ζζ−ζ−ζζ−ζζζ3−ζ3ζ3−ζ3−ζ3ζ3−ζ3ζ3
χ221-1-1111-1-1-111-1-111-1-111-111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111ii−i−iii−i−ii−ii−i−i−iii−i−iii−ζζ−ζζζ−ζζ−ζ−ζ3ζ3−ζ3ζ3ζ3−ζ3ζ3−ζ3
χ231-1-1111-1-1-111-1-111-1-111-111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111−i−iii−i−iii−ii−iiii−i−iii−i−iζ3−ζ3ζ3−ζ3−ζ3ζ3−ζ3ζ3ζ−ζζ−ζ−ζζ−ζζ
χ241-1-1111-1-1-111-1-111-1-111-111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111−i−iii−i−iii−ii−iiii−i−iii−i−i−ζ3ζ3−ζ3ζ3ζ3−ζ3ζ3−ζ3−ζζ−ζζζ−ζζ−ζ
χ251-1-11-1-1111-11ii−i−i−i−iii-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-1111-1-11−i−iiiii−i−i1-1-11i−i−ii1-1-11−iii−i
χ261-1-11-1-1111-11ii−i−i−i−iii-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-1111-1-11−i−iiiii−i−i-111-1−iii−i-111-1i−i−ii
χ271-1-11-1-1111-11ii−i−i−i−iii-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-11111-1-1-111-1ii−i−i−i−iiii−i−ii-111-1−iii−i-111-1
χ281-1-11-1-1111-11ii−i−i−i−iii-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-11111-1-1-111-1ii−i−i−i−iii−iii−i1-1-11i−i−ii1-1-11
χ291-1-11-1-1111-11−i−iiiii−i−i-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-1111-1-11ii−i−i−i−iii1-1-11−iii−i1-1-11i−i−ii
χ301-1-11-1-1111-11−i−iiiii−i−i-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-1111-1-11ii−i−i−i−iii-111-1i−i−ii-111-1−iii−i
χ311-1-11-1-1111-11−i−iiiii−i−i-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-11111-1-1-111-1−i−iiiii−i−ii−i−ii1-1-11−iii−i1-1-11
χ321-1-11-1-1111-11−i−iiiii−i−i-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-11111-1-1-111-1−i−iiiii−i−i−iii−i-111-1i−i−ii-111-1
χ3322222222-2-2-200000000-2222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000022222222-2-2-2-2000000000000000000000000
χ3422222222-2-2-200000000-2222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000-2-2-2-2-2-2-2-22222000000000000000000000000
χ352222-2-2-2-222-200000000-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000002i2i2i2i−2i−2i−2i−2i−2i−2i2i2i000000000000000000000000
χ362222-2-2-2-222-200000000-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000−2i−2i−2i−2i2i2i2i2i2i2i−2i−2i000000000000000000000000
χ3722-2-22i−2i2i−2i0001+i−1−i1+i−1−i1−i−1+i1−i−1+i02222-2-20000-2-20000000000002i2i−2i−2i2i2i−2i−2i1+i1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1−i−1−i1−i1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1+i−1+i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300002−22−2i2−i2i2−i20000000000000000
χ3822-2-22i−2i2i−2i0001+i−1−i1+i−1−i1−i−1+i1−i−1+i02222-2-20000-2-20000000000002i2i−2i−2i2i2i−2i−2i1+i1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1−i−1−i1−i1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1+i−1+i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000−22−22−i2i2−i2i20000000000000000
χ3922-2-22i−2i2i−2i000−1−i1+i−1−i1+i−1+i1−i−1+i1−i02222-2-20000-2-20000000000002i2i−2i−2i2i2i−2i−2i−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1−i1−i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000−22−22−i2i2−i2i20000000000000000
χ4022-2-22i−2i2i−2i000−1−i1+i−1−i1+i−1+i1−i−1+i1−i02222-2-20000-2-20000000000002i2i−2i−2i2i2i−2i−2i−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1−i1−i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300002−22−2i2−i2i2−i20000000000000000
χ4122-2-2−2i2i−2i2i0001−i−1+i1−i−1+i1+i−1−i1+i−1−i02222-2-20000-2-2000000000000−2i−2i2i2i−2i−2i2i2i1−i1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1+i−1+i1+i1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1−i−1−i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000−22−22i2−i2i2−i20000000000000000
χ4222-2-2−2i2i−2i2i0001−i−1+i1−i−1+i1+i−1−i1+i−1−i02222-2-20000-2-2000000000000−2i−2i2i2i−2i−2i2i2i1−i1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1+i−1+i1+i1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1−i−1−i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00002−22−2−i2i2−i2i20000000000000000
χ4322-2-2−2i2i−2i2i000−1+i1−i−1+i1−i−1−i1+i−1−i1+i02222-2-20000-2-2000000000000−2i−2i2i2i−2i−2i2i2i−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1+i1+i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00002−22−2−i2i2−i2i20000000000000000
χ4422-2-2−2i2i−2i2i000−1+i1−i−1+i1−i−1−i1+i−1−i1+i02222-2-20000-2-2000000000000−2i−2i2i2i−2i−2i2i2i−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1−i1−i−1−i−1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1+i1+i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000−22−22i2−i2i2−i20000000000000000
χ452-22-22i−2i−2i2i0001+i−1−i−1−i1+i1−i−1+i−1+i1−i022-2-2220000-2-20000000000002i2i−2i−2i−2i−2i2i2i1+i1+i1+i1+i−1−i−1−i−1−i−1−i−1−i−1−i−1−i−1−i1+i1+i1+i1+i1−i1−i1−i1−i−1+i−1+i−1+i−1+i−1+i−1+i−1+i−1+i1−i1−i1−i1−i2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000i2−i2−i2i2−222−20000000000000000
χ462-22-22i−2i−2i2i0001+i−1−i−1−i1+i1−i−1+i−1+i1−i022-2-2220000-2-20000000000002i2i−2i−2i−2i−2i2i2i1+i1+i1+i1+i−1−i−1−i−1−i−1−i−1−i−1−i−1−i−1−i1+i1+i1+i1+i1−i1−i1−i1−i−1+i−1+i−1+i−1+i−1+i−1+i−1+i−1+i1−i1−i1−i1−i−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000−i2i2i2−i22−2−220000000000000000
χ472-22-22i−2i−2i2i000−1−i1+i1+i−1−i−1+i1−i1−i−1+i022-2-2220000-2-20000000000002i2i−2i−2i−2i−2i2i2i−1−i−1−i−1−i−1−i1+i1+i1+i1+i1+i1+i1+i1+i−1−i−1−i−1−i−1−i−1+i−1+i−1+i−1+i1−i1−i1−i1−i1−i1−i1−i1−i−1+i−1+i−1+i−1+i2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000−i2i2i2−i22−2−220000000000000000
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χ1204-4-44-4-444-44-4000000004-212-12-122-1-1-21-2-21122-1-1-2-2112-12-1-21-2100-3300-33003-3003-3003-3003-300-3300-33000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.